Find the vertical asymptote (V.A.) and the horizontal asymptote (H.A.) of the function g(x) = 2x/...

Find the vertical asymptote (V.A.) and the horizontal asymptote (H.A.) of the function g(x) = 2x/ x- 5.

Justify your answer using limits.

a) The equation of the V.A. is ________ and the associated limit is:

b) The equation of the H.A. is ________ and the associated limit is:

Expert Solution

milcah answered 1 year ago

For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote. f(x) = 2x/(x + 4)

For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote.f(x) = 2x/(x + 4)

For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote. f(x) = 1/x -0 2

For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote.f(x) = 1/x -0 2

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For the following exercises, graph the transformation of f(x) = 2x. Give the horizontal asymptote, the domain, and the range.h(x) = 2x + 3

For the following exercises, graph the transformation of f(x) = 2x. Give the horizontal asymptote, the domain, and the range. f(x) = 2x − 2

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For each function, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal asymptote. 19. p(x)= 2x-3/x+4 21. s(x)=4/(x-2)^2 24. g(x)= 2x^2 +7x - 15/ 3x^2- 14+ 15 26. k(x)= 2x^2- 3x- 20/x-5

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In your own words, describe why the graph of a rational function can cross its horizontal asymptote but it can never cross a vertical asymptote.

Consider the function f(x)= 1 + 1/x - 1/x2 Find the domain, the vertical and horizontal...

Consider the function f(x)= 1 + 1/x - 1/x2 Find the domain, the vertical and horizontal asymptotes, the intervals of increase or decrease, the local minimum and maximum values, the intervals of concavity and the inflection points.

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